1090.71 – Twenty-Seven Little Cubes

I took a white three-inch cube, painted its surface blue, and cut it up into 27 little cubes. The inside of the cube is still white. How many of the 27 little cubes have one blue face? How many have two? How many have Three? More than three?

Solution

With one blue face: 6,

With two blue faces: 12,

Three blue faces: 8,

More than three: 0,

Let's see: 6 + 12 + 8 = 26.

Are we missing a cube?